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A lot of it is statistical fuckery. The set of people hospitalized who are unvaccinated is not the same as the set of unvaccinated people who end up getting hospitalized.

But some of it is certainly true. Vaccination makes a very significant difference in hospitalization among the very at-risk subset of the population. But in the healthier demographics, vaccination status is irrelevant to "net hospitalization" because in those demographics COVID itself is irrelevant to hospitalization when compared to other causes of hospitalization.

Since I didn't mention it explicitly, I mentioned all-cause mortality because that's going to be very correlated to all-cause hospitalization as well (and the fact that mortality itself is something we should care about).